On the Log-Laplace Equation for Nonlocal Operators Generating Sub-Markovian Semigroups

We consider the semilinear Cauchy problem for a class of pseudo-differential operators generating sub-Markovian semigroups. Solutions of such problems with negative definite nonlinearity play an important role in constructing branching measure-valued processes. We establish local existence and uniqueness of solutions in the context of the Dirichlet space associated to the problem. Comparison and global properties of solutions are also studied. Accepted 29 August 2001. Online publication 17 December 2001.     

Martingale property of empirical processes

It is shown that for a large collection of independent martingales, the martingale property is preserved on the empirical processes. Under the assumptions of independence and identical finite-dimensional distributions, it is proved that a large collection of stochastic processes are martingales essentially if and only if the empirical processes are also martingales. These two results have implications on the testability of the martingale property in scientific modeling. Extensions to submartingales and supermartingales are given.

     

The isolation and structure of 6″-bromo-isoarboreol - the first bromine containing lignan

A new lignan from $\text{Gmelina arborea}$ is shown to be 1, 2a-dihydroxy-2e-piperonyl-6e-(6″-bromopiperonyl)-3, 7-dioxabicyclo-[3,3,0]-octane, the first example of a bromine containing lignan.     

Secondary alpha-deuterium kinetic isotope effects: assumptions simplifying interpretations of mechanisms of solvolyses of secondary alkyl sulfonates

For solvolyses of 2-propyl and cyclopentyl sulfonates, logarithms of alpha-deuterium kinetic isotope effects (alpha-KIE) correlate linearly with logarithms of nucleophilic solvent assistance (NSA); correlations have the same slopes, but different intercepts, consistent with both solvent and structural effects on alpha-KIEs for heterolysis, further supported by recent theoretical and experimental data. It is argued that alpha- and beta-KIEs cannot yet distinguish between mechanisms proceeding via one or more transition states of similar energies. Structural, solvent, and isotope effects can be rationalized by heterolysis accompanied by NSA.     

Analysis of urinary nucleosides. I. Optimisation of high performance liquid chromatography/electrospray mass spectrometry

In order to optimise the analysis of urinary nucleosides by high performance liquid chromatography/mass spectrometry (HPLC/MS), the HPLC separation of these compounds was performed at different 'flow rates' and 0.2mL/min was found to give both a better separation and ionisation. The ionisation conditions were optimised to give the best intensity of the molecules quasi-molecular ions. The ion distribution profile and ionisation in both positive and negative mode were examined and the detection of the protonated molecule in positive mode chosen for further analysis. The limits of detection of the method developed are reported and representative LC/MS and LC/MS/MS spectra shown. Typical urinary nucleoside chromatograms are presented.     

The phenolic oxidation of a β-methylchalcone

The phenolic oxidation of 2',4-dihydroxy-4'-methoxy-β-methylchalcone using alkaline potassium ferricyanide gives an aurone rather than an isoflavone. This result is discussed in the context of current theories regarding the biosynthesis of flavonoid and isoflavonoid compounds.     

Synthesis and characterisation of phosphane-substituted Co3C clusters having a pendant allyl side-chain

Substituted μ₃-carbido-capped tricobalt carbonyl clusters have been synthesised by reaction of [Co₃(μ₃-C(O)OCH₂CHCH₂)(CO)₉] with a range of monodentate and chelating phosphane ligands. The products have been characterised by microanalysis, IR and NMR spectroscopy, mass spectrometry and, in the case of [Co₃(μ₃-CR)(CO)₇(dppe)], [Co₃(μ₃-CR)(CO)₇(dppm)], [Co₃(μ₃-CR)(CO)₇(PPh₃)₂], [Co₃(μ₃-CR)(CO)₇(PMe₃)₂] and [Co₃(μ₃-CR)(CO)₆(PEt₃)₃] (R=C(O)OCH₂CHCH₂), single crystal X-ray diffraction.     

Persulphate quenching of the excited state of ruthenium(II) tris-bipyridyl dication: thermal reactions

The rate constant for the reaction between the sulphate radical (SO₄^√−) and the ruthenium (II) tris-bipyridyl dication (Ru(bipy)₃²⁺) is (3.3±0.2)×10⁹ mol⁻¹ dm³ s⁻¹ in 1 mol dm⁻³ H₂SO₄ and (4.9±0.5)×10⁹ mol⁻¹ dm³ s⁻¹ in 0.1 mol dm⁻³, pH 4.7 acetate buffer. The SO₄^√−radical produced by the electron transfer quenching of Ru(bipy)₃^2+* by S₂O₈²⁻ reacts rapidly with both acetate buffer and chloride ions. These side reactions result in a reduction in the overall quantum yield of Ru(bipy)₃³⁺ production and reduced reaction selectivity when Ru(bipy)₃^2+* is quenched by persulphate.